\newproblem{lay:1_1_25}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 1.1.25}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
  Find an equation involving $g$, $h$, and $k$ that makes this augmented matrix correspond to a consistent system.
	\begin{center}
		$\left(\begin{array}{rrr|r}
		   1 &  -4 &  7 &  g \\
		   0 &   3 & -5 &  h \\
		  -2 &   5 & -9 &  k \\
		\end{array}\right)$
	\end{center}
}{
   % Solution
	We apply row operations to reduce this augmented matrix
	\begin{center}
		\begin{tabular}{cc}
			 $\mathbf{r}_3\leftarrow \mathbf{r}_3+2\mathbf{r}_1$ &
				$\left(\begin{array}{rrr|r}
					 1 &  -4 &  7 &  g \\
					 0 &   3 & -5 &  h \\
					 0 &  -3 &  5 &  2g+k \\
				\end{array}\right)$\\
			 $\mathbf{r}_3\leftarrow \mathbf{r}_3+\mathbf{r}_2$ &
				$\left(\begin{array}{rrr|r}
					 1 &  -4 &  7 &  g \\
					 0 &   3 & -5 &  h \\
					 0 &   0 &  0 &  2g+k+h \\
				\end{array}\right)$
		\end{tabular}
	\end{center}
  The system is compatible only if $2g+k+h=0$. In this case, the system has infinite solutions since it is compatible indeterminate.
}
\useproblem{lay:1_1_25}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
